N - mixture models by species

modelling N by site to get relative abundance

abundance by site will be used as a cov on predator occupancy

7 models evaluated, dot, jdt + jdtSQ, lure + jdt + jdtSQ


Species:      WhiteTailedJackrabbit



Metadata Summary:

N_sites N_counts N_detections rep_period iterations burnin thin
127 283 181 7 days 120000 20000 10



Detections by Year:

Yr 2016 2017 2018 2019 2020
sites 19 31 19 32 26
detections 19 39 43 57 23
N.dot.model 7 17 19 18 7



WAIC

Models by WAIC:
model description WAIC N.total.est
fm7 counts 3.962858 127
fm2 jdt 1116.837448 71
fm5 jdt + jdtSq 1117.412453 73
fm4 lure + jdt 1118.211814 72
fm6 lure + jdt + jdtSq 1118.662959 73
fm1 dot 1119.959703 68
fm3 lure 1119.983799 70



Model summaries:



model: fm1
dot



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
p[1] NA 6368 0.113 0.108 0.06 0.16 0 1.001
p[2] NA 4102 0.091 0.089 0.05 0.13 0 1.001
p[3] NA 3343 0.052 0.05 0.03 0.07 0 1.001
p[4] NA 5495 0.091 0.087 0.06 0.12 0 1.001
p[5] NA 7630 0.081 0.078 0.05 0.11 0 1.001
lambda[1] NA 6607 0.447 0.354 0.15 0.70 0 1.001
lambda[2] NA 3939 0.767 0.643 0.39 1.12 0 1.001
lambda[3] NA 3527 1.305 1.095 0.62 1.98 0 1.001
lambda[4] NA 7079 0.687 0.636 0.38 0.98 0 1.001
lambda[5] NA 8273 0.339 0.287 0.12 0.54 0 1.001
N[107] NA 10000 0.024 err 0.00 0.00 err err
N[12] NA 10041 0.038 err 0.00 0.00 err err
N[72] NA 10000 0.102 err 0.00 0.00 err err
N[21] NA 7953 1.123 err 1.00 2.00 err err
N[20] NA 7924 1.244 err 1.00 2.00 err err

p[1]

p[2]

p[3]

p[4]

p[5]

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[107]

N[12]

N[72]

N[21]

N[20]







model: fm2
jdt



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha jdt 9422 -0.170 -0.153 -0.31 -0.04 0.14777 0.9777
alpha0 NA 4910 -2.524 -2.528 -2.73 -2.31 0 1.001
lambda[1] NA 8915 0.581 0.491 0.24 0.91 0 1.001
lambda[2] NA 7599 0.815 0.743 0.47 1.14 0 1.001
lambda[3] NA 9506 0.927 0.832 0.52 1.30 0 1.001
lambda[4] NA 7941 0.772 0.719 0.43 1.06 0 1.001
lambda[5] NA 9235 0.330 0.288 0.13 0.51 0 1.001
N[115] NA 10000 1.061 err 1.00 1.00 err err
N[16] NA 9629 0.103 err 0.00 0.00 err err
N[61] NA 10000 1.047 err 1.00 1.00 err err
N[58] NA 10000 1.054 err 1.00 1.00 err err
N[47] NA 9259 0.102 err 0.00 0.00 err err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[115]

N[16]

N[61]

N[58]

N[47]

alpha relationship







model: fm3
lure



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha lure 9489 -0.008 -0.022 -0.17 0.15 0.97272 0.5296
alpha0 NA 5189 -2.505 -2.496 -2.70 -2.29 0 1.001
lambda[1] NA 9306 0.538 0.484 0.21 0.84 0 1.001
lambda[2] NA 8281 0.826 0.735 0.47 1.15 0 1.001
lambda[3] NA 9136 0.942 0.912 0.52 1.32 0 1.001
lambda[4] NA 8953 0.763 0.714 0.45 1.06 0 1.001
lambda[5] NA 8590 0.339 0.282 0.13 0.54 0 1.001
N[46] NA 9660 1.508 1 1.00 2.00 0 1.0001
N[83] NA 10143 0.136 err 0.00 1.00 err err
N[47] NA 8777 0.105 err 0.00 0.00 err err
N[5] NA 8795 1.828 2.002 1.00 3.00 0 1.0005
N[97] NA 9238 0.026 err 0.00 0.00 err err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[46]

N[83]

N[47]

N[5]

N[97]

alpha relationship







model: fm4
lure + jdt



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] lureDays 8616 0.067 0.077 -0.11 0.24 0.8109 0.7267
alpha[2] julianDt 8670 -0.191 -0.213 -0.35 -0.05 0.12979 0.9817
alpha0 NA 4975 -2.521 -2.491 -2.74 -2.33 0 1.001
lambda[1] NA 9012 0.602 0.497 0.23 0.93 0 1.001
lambda[2] NA 8585 0.829 0.786 0.49 1.17 0 1.001
lambda[3] NA 9022 0.927 0.863 0.53 1.32 0 1.001
lambda[4] NA 8191 0.774 0.736 0.47 1.08 0 1.001
lambda[5] NA 10000 0.325 0.272 0.12 0.51 0 1.001
N[77] NA 10000 0.125 err 0.00 1.00 err err
N[52] NA 10000 0.044 err 0.00 0.00 err err
N[58] NA 10000 1.059 err 1.00 1.00 err err
N[105] NA 10000 1.030 err 1.00 1.00 err err
N[127] NA 9473 0.017 err 0.00 0.00 err err

alpha[1]

alpha[2]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[77]

N[52]

N[58]

N[105]

N[127]







model: fm5
jdt + jdtSq



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] julianDt 4659 0.094 0.106 -0.12 0.35 0.89194 0.7388
alpha[2] julianDtSq 4072 -0.382 -0.399 -0.64 -0.11 0.07627 0.9906
alpha0 NA 4605 -2.588 -2.581 -2.80 -2.37 0 1.001
lambda[1] NA 9300 0.552 0.465 0.22 0.86 0 1.001
lambda[2] NA 7575 0.888 0.849 0.51 1.22 0 1.001
lambda[3] NA 7938 0.924 0.857 0.51 1.30 0 1.001
lambda[4] NA 7826 0.834 0.769 0.49 1.16 0 1.001
lambda[5] NA 10000 0.333 0.27 0.13 0.52 0 1.001
N[45] NA 10000 1.674 1 1.00 3.00 0 1.0003
N[57] NA 8748 2.367 2.002 2.00 4.00 0 1.0009
N[126] NA 9377 0.019 err 0.00 0.00 err err
N[32] NA 10000 0.065 err 0.00 0.00 err err
N[59] NA 10000 0.051 err 0.00 0.00 err err

alpha[1]

alpha[2]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[45]

N[57]

N[126]

N[32]

N[59]

julian date relationship







model: fm6
lure + jdt + jdtSq



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] lureDays 5900 -0.037 -0.037 -0.22 0.15 0.96177 0.6223
alpha[2] julianDt 3266 0.115 0.078 -0.14 0.37 0.80197 0.7626
alpha[3] julianDtSq 3316 -0.401 -0.399 -0.68 -0.13 0.07549 0.9893
alpha0 NA 4247 -2.593 -2.585 -2.80 -2.37 0 1.001
lambda[1] NA 8777 0.545 0.475 0.22 0.86 0 1.001
lambda[2] NA 7738 0.881 0.84 0.51 1.23 0 1.001
lambda[3] NA 8437 0.918 0.885 0.53 1.30 0 1.001
lambda[4] NA 7867 0.831 0.771 0.49 1.15 0 1.001
lambda[5] NA 9498 0.339 0.276 0.13 0.53 0 1.001
N[78] NA 10000 0.270 err 0.00 1.00 err err
N[30] NA 9420 1.359 1 1.00 2.00 0 1
N[42] NA 9710 0.255 err 0.00 1.00 err err
N[57] NA 8810 2.341 2.002 2.00 4.00 0 1.0009
N[44] NA 9480 0.360 0 0.00 1.00 1 err

alpha[1]

alpha[2]

alpha[3]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[78]

N[30]

N[42]

N[57]

N[44]







model: fm7
counts



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha counts 8243 7.653 7.24 5.56 9.55 0 1.001
alpha0 NA 9596 -7.163 -6.841 -8.80 -5.59 0 1.001
lambda[1] NA 8812 0.975 0.808 0.34 1.54 0 1.001
lambda[2] NA 9695 0.982 0.907 0.56 1.36 0 1.001
lambda[3] NA 10000 0.991 0.957 0.53 1.41 0 1.001
lambda[4] NA 10000 0.988 0.94 0.55 1.40 0 1.001
lambda[5] NA 7503 0.964 0.794 0.34 1.53 0 1.001
N[115] NA 0 1.000 err 1.00 1.00 err err
N[108] NA 10000 1.000 err 1.00 1.00 err err
N[86] NA 0 1.000 err 1.00 1.00 err err
N[99] NA 0 1.000 err 1.00 1.00 err err
N[110] NA 10000 0.960 0 0.00 2.00 1 err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[115]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[108]

N[86]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[99]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[110]

alpha relationship